This is how we add


Step 1Can you add yet? Nope! The denominators don't match. We need a common denominator. So next we take both denominators and multiply them. Next, take each numerator and multiply it by the denominator of the other term. So, we multiply 4 by 12, and get 48, then we multiply 10 by 12 and get 120. Now for the second term. You multiply 5 by 10, and get 50, then multiply 10 by 12 and get 120. We now have a new problem, that looks like this:


Step 2Since our denominators match, we can add the numerators. 48 + 50 = 98 That gives us the sum, which is


Step 3Now, do we need to simplify this fraction? First, we attempt to divide it by 2... Are both the numerator and the denominator evenly divisible by 2? Yes! So we reduce it:
Now, try the same number again. Nope. Try the next prime number, 3... Nope. Try the next prime number, 5... Nope. Try the next prime number, 7... Nope. Try the next prime number, 11... Nope. Try the next prime number, 13... Nope. Try the next prime number, 17... Nope. Try the next prime number, 19... Nope. Try the next prime number, 23... Nope. Try the next prime number, 29... Nope. Try the next prime number, 31... Nope. Try the next prime number, 37... Nope. Try the next prime number, 41... Nope. Try the next prime number, 43... Nope. Try the next prime number, 47... Nope. Try the next prime number, 53... No good. 53 is larger than 49. So we're done reducing. Congratulations! Here's your final answer to 4/10 + 5/12
